Question

rozwiaz rownania:

Answer 1

a) a1=1

r = 3

Sn= 1/2(a1+an)*n = 8n

1/2(a1+an)*n = 8n/*2

(a1+ a1 + (n-1)*r)n = 16n

(2 + 3(n-1))* n = 16n   /: n  n różne od 0

2+3n-3 =16

3n = 16+1  /: 3

n = 17/3 - odrzucamy, bo n jest l. naturalną 

odp. Brak rozwiązań

 

b)a1= 3

    r = 4

Sn = 1/2(a1+an)*n = 465  /*2

            (a1 + a1 +(n-1)*r)*n =930

             (6+4(n-1))*n = 930

               6n+ 4n^2 -4n - 930 = 0

4n^2+ 2n -930 = 0   /:2

2n^2 + n - 465 = 0

delta = 1^2 + 4*2*465 = 1+ 3720 =3721

pierw. z delty = 61

n1 = (-1-61)/2*2 = -62/4 - odrzucamy

n2 = (-1+61)/2*2 = 60/4 = 15

Odp. n= 15